Showing papers on "Symmetry (physics) published in 1993"

Forced thermal ratchets.

Abstract: We consider a Brownian particle in a periodic potential under heavy damping. The second law forbids it from displaying any net drift speed, even if the symmetry of the potential is broken. But if the particle is subject to an external force having time correlations, detailed balance is lost and the particle can exhibit a nonzero net drift speed. Thus, broken symmetry and time correlations are sufficient ingredients for transport.

A calculation strategy for the structure determination of symmetric dimers by 1H NMR

Abstract: The structure determination of symmetric dimers by NMR is impeded by the ambiguity of inter- and intramonomer NOE crosspeaks. In this paper, a calculation strategy is presented that allows the calculation of dimer structures without resolving the ambiguity by additional experiments (like asymmetric labeling). The strategy employs a molecular dynamics-based simulated annealing approach to minimize a target function. The experimental part of the target function contains distance restraints that correctly describe the ambiguity of the NOE peaks, and a novel term that restrains the symmetry of the dimer without requiring the knowledge of the symmetry axis. The use of the method is illustrated by three examples, using experimentally obtained data and model data derived from a known structure. For the purpose of testing the method, it is assumed that every NOE crosspeak is ambiguous in all three cases. It is shown that the method is useful both in situations where the structure of a homologous protein is known and in ab initio structure determination. The method can be extended to higher order symmetric multimers.

Exploiting Symmetry In Temporal Logic Model Checking

Abstract: In practice, finite state concurrent systems often exhibit considerable symmetry. We investigate techniques for reducing the complexity of temporal logic model checking in the presence of symmetry. In particular, we show that symmetry can frequently be used to reduce the size of the state space that must be explored during model checking. In the past, symmetry has been exploited in computing the set of reachable states of a system when the transition relation is represented explicitly [13, 10, 17]. However, this research did not consider arbitrary temporal properties or the complications that arise when BDDs are used in such procedures. We have formalized what it means for a finite state system to be symmetric and described techniques for reducing such systems when the transition relation is given explicitly in terms of states or symbolically as a BDD. Moreover, we have identified an important class of temporal logic formulas that are preserved ander this reduction. Our paper also investigates the complexity of various critical steps, like the computation of the orbit relation, which arise when symmetry is used in this type of verification. Finally, we have tested our ideas on a simple cache-coherency protocol based on the IEEE Futurebus+ standard.

Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry

Abstract: We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the underlying noncommutative geometry, a length and a momentum scale appear, leading to the existence of minimal nonzero uncertainties in the positions and momenta. The usual quantum mechanical behaviour is recovered as a limiting case for not too small and not too large distances and momenta.

Dimensional Scaling in Chemical Physics

Abstract: I: Basic Aspects. 1. Introduction. 2. Tutorial. II: The Research Frontier. 3. large-D Limit for N-Electron Atoms. 4. Low D Regime. 5. Hyperspherical Symmetry. 6. Hypercylindrical Symmetry. 7. General Computational Strategies. 8. Two-Electron Excited States. 9. Large-D Limit for Metalic Hydrogen. 10. D-Interpolation of Virial Coefficients. III: Related Methods. 11. Nonseparable Dynamics. 12. Pseudomolecular Electron Correlation in Atoms. Index.

Phase transitions in anisotropically confined ionic crystals.

Abstract: Crystalline, confined ionic systems exhibit well defined phase transitions as a function of the anisotropy of the confining potential. The transitions from one to two dimensions, from two to three, and back from three to two have been investigated as a function of this anisotropy with molecular dynamics simulations. The anisotropy at which such transitions occur seems to be proportional to a power of the number of confined ions.

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Abstract: Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.

Algebraic model for the evolution of the genetic code

Abstract: A search for symmetries based on the compact simple Lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry. An exact continuous symmetry group cannot be found to reproduce the present genetic code. However, a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon. In order to obtain the actual genetic code, the symmetry must be slightly broken.

Preserving symmetries in the proper orthogonal decomposition

Abstract: The proper orthogonal decomposition (POD) (also called Karhunen–Loeve expansion) has been recently used in turbulence to derive optimally fast converging bases of spatial functions, leading to efficient finite truncations. Whether a finite number of these modes can be used in numerical simulations to derive an “accurate” finite set of ordinary differential equations, over a certain range of bifurcation parameter values, still remains an open question. It is shown here that a necessary condition for achieving this goal is that the truncated system inherit the symmetry properties of the original infinite-dimensional system. In most cases, this leads to a systematic involvement of the symmetry group in deriving a new expansion basis called the symmetric POD basis. The Kuramoto–Sivashinsky equation with periodic boundary conditions is used as a paradigm to illustrate this point of view. However, the conclusion is general and can be applied to other equations, such as the Navier–Stokes equations, the complex G...

Baryon-Pion Couplings from Large-N QCD

Abstract: We derive a set of consistency conditions for the pion-baryon coupling constants in the large-N limit of QCD. The consistency conditions have a unique solution which are precisely the values for the pion-baryon coupling constants in the Skyrme model. We also prove that non-relativistic $SU(2N_f)$ spin-flavor symmetry (where $N_f$ is the number of light flavors) is a symmetry of the baryon-pion couplings in the large-N limit of QCD. The symmetry breaking corrections to the pion-baryon couplings vanish to first order in $1/N$. Consistency conditions for other couplings, such as the magnetic moments are also derived.

Gravitational observables and local symmetries.

Abstract: Using a recent classification of local symmetries of the vacuum Einstein equations, it is shown that there can be no observables for the vacuum gravitational field (in a closed universe) built as spatial integrals of local functions of Cauchy data and their derivatives.

Symmetry classes of variable coefficient nonlinear Schrodinger equations

Abstract: A variable-coefficient nonlinear Schrodinger (VCNLS) equation, involving three arbitrary complex functions of space-time (in 1 + 1 dimensions) is analysed from the point of view of its symmetries. All equations of the type studied having non-trivial Lie point symmetry groups G are identified. The symmetry group is shown to be at most five-dimensional and only when the equation is equivalent to the NLS equation itself or to a rather special complex Ginzburg-Landau equation. Lie point transformations are used to obtain solutions of specific VCNLS equations that should be of interest in nonlinear optics or other branches of physics.

Axial symmetry and conformal Killing vectors

Abstract: Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, the authors prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others must vanish or else the symmetry is larger than that originally considered. The results are completely general, and do not depend on Einstein's equations or any particular matter content.

Squeezed states for general systems.

Abstract: We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-order method.

Axial Vector Duality as a Gauge Symmetry and Topology Change in String Theory

Abstract: Lines generated by marginal deformations of WZW models are considered. The Weyl symmetry at the WZW point implies the existence of a duality symmetry on such lines. The duality is interpreted as a broken gauge symmetry in string theory. It is shown that at the two end points the axial and vector cosets are obtained. This shows that the axial and vector cosets are equivalent CFTs both in the compact and the non-compact cases. Moreover, it is shown that there are $\s$-model deformations that interpolate smoothly between manifolds with different topologies.

Hidden symmetry algebra and overlap coefficients for two ring-shaped potentials

Abstract: A new approach is proposed to general systems possessing SU(1,1)(+)SU(1,1) dynamical symmetry. On the base of this approach, the quadratic Hahn algebra QH(3) is shown to serve as a hidden symmetry (in both quantum and classical pictures) for two potentials generalizing the Hartmann and the oscillator ring-shaped potentials. The overlap coefficients between wavefunctions in spherical and parabolic (cylindrical) coordinates are shown to coincide with Clebsch-Gordan coefficients for SU(1,1) algebra.

Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum

Abstract: We present a comprehensive normal-mode decomposition analysis for the recently introduced [ J. Opt. Soc. Am. A10, 95 ( 1993)] class of twisted Gaussian Schell-model fields in partially coherent beam optics. The formal analogies to quantum mechanics in two dimensions are exploited. We also make effective use of a dynamical SU(2) symmetry of these fields to achieve the mode decomposition and to determine the spectrum. The twist phase is nonseparable in nature, rendering it nontrivially two dimensional. The consequences of this, resulting in the need to use Laguerre–Gaussian functions rather than products of Hermite–Gaussians, are carefully analyzed. An important identity involving these sets of special functions is established and is used in deriving the spectrum.

1/N Corrections to the Baryon Axial Currents in QCD

Abstract: We prove that the 1/N corrections to the baryon axial current matrix elements are proportional to their lowest order values. This implies that the first correction to axial current coupling constant ratios vanishes, and that the $SU(2N_f)$ spin-flavor symmetry relations are only violated at second order in 1/N.

Construction of exact solutions of the Einstein-Maxwell equations corresponding to a given behaviour of the Ernst potentials on the symmetry axis

Abstract: The method developed by one of the authors for the construction of exact solutions of the Einstein-Maxwell equations by setting the behaviour of the Ernst potentials on the symmetry axis is discussed in full detail. Some new results regarding the solution of the integral equations and the construction of the 3*3 matrix potential H are presented. Two new examples of the application of the method are considered, one of which is the stationary vacuum solution for a rotating mass, and the second one is the four-parameter metric which can be used for the description of the exterior field of a charged magnetized spinning source.

Thermal fluctuations in a pair of magnetostatically coupled particles

Abstract: The influence of the thermal agitation on the switching dynamics for a pair of identical uniaxially anisotropic dipoles is studied for the case of the applied field parallel to the bond direction and the common anisotropy axis. A set of Langevin equations was derived from the micromagnetic energy expression and solved numerically. The switching behavior resembles a random walk over the energy barrier arising from the anisotropy of the system. The relaxation time is computed as a function of temperature, applied field, and coupling strength. The temperature dependence of the maximum energy of the fluctuations provides a method of evaluating the energy barrier of reversal. The thermal agitation is shown to reduce the symmetry of the ‘‘fanning’’ reversal mode.

Nonlinear optical solitary waves in a photonic band gap

Abstract: It is suggested that solitary wave solutions exist in the gap region of photonic band gap materials with a Kerr nonlinearity. Using a variational trial function we estimate the amplitude, size scale, and the nature of phase modulation of these nonlinear waves. In two dimensions, we predict the occurrence of a variety of finite energy solitary waves associated with the different symmetry points of the crystalline Brillouin zone. Solutions which preserve the symmetry of the crystal exist for both positive and negative Kerr coefficient whereas solutions which break the symmetry occur only for positive nonlinearity. These states are relevant to the bistable switching properties of photonic band gap materials.

Symmetries of the Kadomtsev-Petviashvili equation

Abstract: Generalized symmetries with arbitrary functions of time t for the well known 2+1-dimensional integrable model, Kadomtsev-Petviashvili (KP) equation, are found by means of the extended mastersymmetry approach. Then an explicit and simple constructive formula for the symmetries of the KP equation is derived directly from the symmetry definition equation, without using complicated recursion operators. All the known symmetries appear as special cases of those obtained in this paper. The general infinite-dimensional Lie algebra constituted by these symmetries is also given.

Molecular Mechanics Calculations of Giant- and Hyperfullerenes with Eicosahedral Symmetry

Abstract: Structures and energies of the first few members of giant- and hyperfullerenes with Ih symmetry have been calculated by using MM3.